Are any P2P platforms actually safe from data breaches?

Putting aside any specific platform for a minute, no company in the world is safe from this. The NSA, arguably one of the best funded* and most IT security conscious* organisations on the planet has had data taken from it. If they can't stop it, no one can. The real question is recovery actions. If it's a bank and your cash is stolen, you have the Fscs guarantee to fall back on. Peer2x companies, not so much. Platform failure should be considered as part of your assessment of where to put money.

On a more practical nature, if the above applied in the U.K., Tesco bank, the DVLA, various hospitals, talk talk, yahoo etc etc would all be closed down. We would have very few organisations left if a 'one strike' rule was applied.

All that said, I agree that there is almost always more any organisation can do to reduce the risk of this happening, or the impact if it does happen, or improve the recovery processes from it happening. All of these should be encouraged to a degree. Not to infinity, as that would drive them out of business due to costs and slowness of delivery, as with everything there is a trade off.

*Im guessing.

I'm intrigued. How would blockchain protect people's personal information?

The only way I can see for companies to be immune from data breaches is not to hold any data about their customers. The FCA might be a little uneasy about that.